We will use the Heyneman–Sweedler-type notation
\(\ell (h)=:\ell (h)^{\langle 1 \rangle }\otimes \ell (h)^{\langle 2 \rangle }\) 
with the summation sign suppressed.
One can easily prove (see [1]} and references therein) that
a comodule algebra is principal if and only if it admits a strong
connection.
Here we need the following slight generalization of this fact:
